WO2020019782A1 - 一种预测混凝土顺筋开裂后预应力损失方法 - Google Patents

一种预测混凝土顺筋开裂后预应力损失方法 Download PDF

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WO2020019782A1
WO2020019782A1 PCT/CN2019/084103 CN2019084103W WO2020019782A1 WO 2020019782 A1 WO2020019782 A1 WO 2020019782A1 CN 2019084103 W CN2019084103 W CN 2019084103W WO 2020019782 A1 WO2020019782 A1 WO 2020019782A1
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concrete
formula
force
stress
steel strand
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PCT/CN2019/084103
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French (fr)
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王磊
戴理朝
张建仁
张旭辉
马亚飞
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长沙理工大学
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N33/00—Investigating or analysing materials by specific methods not covered by groups G01N1/00 - G01N31/00
    • G01N33/38—Concrete; Lime; Mortar; Gypsum; Bricks; Ceramics; Glass
    • G01N33/383—Concrete or cement
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N17/00—Investigating resistance of materials to the weather, to corrosion, or to light
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/06—Power analysis or power optimisation

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  • the invention relates to the technical field of prestress loss evaluation methods, and in particular to a method for predicting prestress loss after cracking of concrete along a tendon.
  • prestressed concrete members For a long time, prestressed concrete members have been considered to have good durability. However, due to factors such as design defects, poor construction, and unfavorable erosion environment, the performance degradation of prestressed concrete members has become increasingly significant. Corrosion of prestressed tendons is one of the main factors that cause the degradation of structural durability. Corrosion will reduce the cross-sectional area of prestressed tendons, cause cracking of concrete, reduce the bonding strength, and cause the loss of effective prestressing. Reasonable evaluation of the effective prestress inside the concrete component is the key factor to ensure its normal use and safe service.
  • the prestress loss of existing concrete components is related to many factors, such as shrinkage and creep of concrete, stress relaxation and corrosion of prestressed steel strands.
  • shrinkage and creep of concrete stress relaxation and corrosion of prestressed steel strands.
  • prestressed steel strand stress relaxation and other factors on long-term prestress loss and some specifications also give evaluation methods of long-term prestress loss.
  • Relative to the reports of long-term prestressing loss of concrete members there are relatively few studies on corrosion prestressing loss.
  • Some researchers have used strain coordination to evaluate the residual prestressing force of post-tensioned concrete beams, and some researchers have pointed out that the residual pre-stressing force of post-tensioned concrete beams can be estimated by the cross-sectional area of corroded steel strands.
  • the existing research mainly analyzes the influence of the reduction of cross-sectional area of corroded steel strands on the prestress loss of post-tensioned concrete members.
  • the prestress loss caused by the corrosion of steel strands is a very complicated problem. Not only the reduction of the cross-sectional area of steel strands will cause the prestress loss, but also the rust expansion and cracking of the concrete and the bond strength will also cause the prestress loss.
  • post-tensioned concrete members rely on the anchoring system for pre-stress transmission, while pre-tensioned pre-stressed concrete members perform pre-stress transmission through the bonding force between steel strands and concrete. Corrosion bond degradation is effective for pre-tensioned concrete members.
  • the present invention proposes a method for predicting the prestress loss of concrete after cracking along the tendons.
  • the advantage of this method is that it can comprehensively consider the effects of factors such as concrete cracking and bond degradation caused by corrosion on the internal prestress loss of pretensioned concrete members. .
  • the purpose of the present invention is to provide a method for predicting the prestress loss of concrete after cracking along the tendons, which can reasonably evaluate the prestress loss inside the rusted pretensioned concrete member.
  • a method for predicting the prestress loss of concrete after cracking along the tendons including the following steps:
  • Prediction of concrete swell and cracking According to the basic size of the component, determine the value of geometric parameters, and use the thick wall and thin cylinder theory to simulate the concrete swell and cracking. During the rust and cracking process, the residual tensile stress and Binding force of cracked concrete to predict rust expansion force;
  • the rust expansion force of the concrete during rust expansion cracking is calculated as follows:
  • the rust expansion force P c between the steel strand and the concrete interface can be expressed as formula (1):
  • R 0 is the radius of the steel wire before corrosion
  • Pu is the rust expansion force at the interface of the cracked and uncracked concrete
  • Ru is the radius of the cracked concrete
  • r is the position of the cracked concrete area
  • ⁇ ⁇ (r) is Hoop stress of cracked concrete
  • the rust expansion force P c between the steel strand and the concrete interface can be expressed as formula (2):
  • the calculation of the bonding strength of the corroded steel strand is as follows:
  • the bonding strength of corroded steel strands is mainly provided by the adhesive force, binding force and rust expansion force at the interface between the steel strands and concrete, and its expression is formula (3):
  • ⁇ ⁇ ⁇ a + ⁇ b + ⁇ c
  • ⁇ ⁇ is the bonding stress of corroded steel strands
  • ⁇ a is the bonding stress caused by rust expansion force
  • ⁇ b is the adhesion force at the interface
  • ⁇ c is the constraint force at the interface
  • k c is the friction coefficient between the corroded steel strand and the concrete interface
  • k is the number of transverse ribs of the strand on the same section
  • a r is the area of the transverse rib
  • D is the diameter of the corroded strand
  • ⁇ is the angle between the transverse rib and the axis of the strand
  • ⁇ is the strand
  • s r is the distance between the transverse ribs
  • f coh is the adhesion force coefficient between the interfaces
  • the binding force of the concrete around the interface between the corroded steel strand and the concrete can be expressed as formula (6):
  • C r is the shape coefficient of the transverse ribs
  • p x is the maximum pressure on the steel strand when it fails.
  • the calculation method of the effective prestress of the rusted pretensioned concrete member is as follows:
  • the pre-tensioned concrete member is separated into multiple differential units, and the differential units are numbered from 1 to n.
  • the stress f p, i of the internal steel strand can be expressed as formula (7):
  • ⁇ f p, i is the local stress variable of the corroded steel strand unit i, 1 ⁇ i ⁇ n;
  • the local stress variable ⁇ f p, i of element i can be expressed as formula (8):
  • ⁇ ⁇ is the bonding stress of the corroded steel strand
  • l i is the unit length
  • Ap, i ( ⁇ ) is the remaining cross-sectional area of the corroded steel strand at the position of unit i
  • R ⁇ , i is the position of unit i The remaining radius of the rusted wire
  • the tensile force T p, i of the corroded steel strand at the position of unit i can be expressed as formula (10):
  • T pi is the initial pre-stressing force of the unrusted steel strand
  • E p is the elastic modulus of the steel strand
  • the stress inside the corroded steel wire gradually increases along the component direction until the effective prestress is reached.
  • the strain change of the concrete at the position of the steel wire ⁇ c, i needs to be equal to the corroded steel wire
  • the strain change ⁇ p, i satisfies the strain coordination relationship, and the relationship is formula (12):
  • a method for predicting the prestress loss of concrete after cracking along the tendons provided by the present invention is used to simulate rust expansion and cracking of concrete by using the theory of thick-walled thin cylinders, based on the residual tensile stress of cracked concrete and uncracked
  • the binding force of the concrete is used to calculate the rust expansion force during the cracking process; the influence of the corrosion of the steel strands on the adhesion between the interface, the concrete restraint force and the rust expansion force is analyzed, and the calculation expression of the bond strength of the corroded steel strands is constructed.
  • Figure 1 is a schematic diagram of concrete cracking caused by corrosion of the steel strand of the present invention
  • FIG. 2 is a change of internal stress of the rusted steel strand of the present invention
  • FIG. 4 is a schematic diagram of a calculation process of rust prestress loss according to the present invention.
  • Figure 5 is the detailed dimensions of the test beam of the present invention.
  • FIG. 6 is a schematic diagram of a four-point bending loading test according to the present invention.
  • FIG. 7 (a) is a prediction value and a test value of the effective prestress of the group A of the present invention.
  • Fig. 7 (b) is the predicted value and the experimental value of the effective prestress of the group B of the present invention.
  • the invention discloses a method for predicting the prestress loss of concrete after cracking along the tendons, which includes the following steps:
  • Prediction of concrete swell and cracking According to the basic size of the component, determine the value of geometric parameters, and use the thick wall and thin cylinder theory to simulate the concrete swell and cracking. During the rust and cracking process, the residual tensile stress and The restraining force of cracked concrete predicts the rust expansion force.
  • R 0 and R ⁇ are the radii of the steel wire before and after rusting, respectively, and A p is the cross-sectional area of the uncorroded steel strand.
  • the volume of the corrosion product of the steel strand is larger than the volume of the correspondingly consumed iron, which causes the outward expansion of the corrosion product.
  • One part of the corrosion products will fill the pores and cracks inside the concrete, and the other part will produce rusty force.
  • the total volume of the corrosion products of steel strands per unit length can be expressed as formula (2):
  • ⁇ V t is the total volume of rust products per unit length
  • ⁇ V t n ⁇ V w
  • n the rust expansion rate, and its value is taken as 3
  • ⁇ V w is the volume change of the outer steel wire of the strand on the unit length
  • ⁇ V e is the volume change of concrete per unit length
  • R t is the radius of the wire including the influence of the rust products
  • ⁇ V c is the volume of the rust products filled with cracks and pores per unit length.
  • Ru is the radius of cracked concrete.
  • the concrete protective layer is composed of a cracked inner ring and an uncracked outer ring, as shown in FIG. 1.
  • elastic theory can be used to simulate the internal stress of the concrete.
  • the hoop stress ⁇ ⁇ (t) and the radial displacement u (t) of the uncracked concrete can be expressed as formulas (5) and (6), respectively. ):
  • t uncracked concrete region
  • R c R o + C
  • C is the thickness of concrete
  • P u is the position of the interface and cracking of concrete uncracked Expansion Force
  • E c and v c are the elastic modulus and Poisson's ratio of the concrete, respectively.
  • r is the position of the crack region concrete, R 0 ⁇ r ⁇ R u.
  • ⁇ ⁇ (r) and ⁇ ⁇ (r) are the hoop stress and strain of the concrete
  • ⁇ ct is the corresponding strain when the concrete reaches tensile strength
  • ⁇ 1 is the concrete stress when the concrete stress is 15% tensile strength.
  • ⁇ u is the ultimate strain of the concrete.
  • R 0 is the radius of the wire before the corrosion
  • R u is a concrete crack radius
  • r is the position of the crack region concrete.
  • the rust expansion force P c of the steel strand-concrete interface can be expressed as formula (11):
  • the calculation method of the bonding strength of the rusted steel strand in the step (2) is:
  • the bonding strength of the corroded steel strand can be calculated from the adhesion force, binding force and rust expansion force at the interface between the strand and the concrete, and its expression is as shown in formula (12):
  • ⁇ ⁇ ⁇ a + ⁇ b + ⁇ c
  • ⁇ ⁇ is the bonding stress of corroded steel strands
  • ⁇ a is the bonding stress caused by rust expansion force
  • ⁇ b is the adhesion force at the interface
  • ⁇ c is the binding force at the interface.
  • k c is the friction coefficient between the corroded steel strand and the concrete interface
  • k c 0.37-0.26 (xx cr )
  • x is the corrosion depth of the steel strand
  • x cr is the critical corrosion depth of the protective layer crack.
  • ⁇ 45 °
  • ⁇ is the friction angle between the steel strand and the concrete
  • tan ( ⁇ + ⁇ ) 1.57-0.785x
  • s r is the distance between the transverse ribs
  • s r 0.6D
  • the binding force of the concrete around the interface between the corroded steel strand and the concrete can be expressed as formula (15):
  • C r is the shape coefficient of the transverse rib
  • C r 0.8
  • p x is the maximum pressure on the steel strand when it fails.
  • the calculation method of the effective prestress in the step (3) is:
  • the pre-tensioned concrete member is separated into multiple differential units, and the differential units are numbered 1 to n.
  • Figure 2 shows a schematic diagram of the internal stress transfer of the corroded steel strand.
  • the stress f p, i of the internal strand Can be expressed as formula (16):
  • ⁇ f p, i is a local stress variable of the corroded steel strand unit i, 1 ⁇ i ⁇ n.
  • the local stress variable ⁇ f p, i of element i can be expressed as formula (17):
  • l i is the length of the unit
  • Ap, i ( ⁇ ) is the remaining cross-sectional area of the corroded steel strand at the position of the unit i
  • R ⁇ , i is the remaining radius of the corroded steel wire at the position of the unit i.
  • the tensile force T p, i of the corroded steel strand at the position of unit i can be expressed as formula (19):
  • strain change ⁇ p, i before and after the corrosion of the steel strand at the location of the unit i can be expressed as formula (20):
  • T pi is the initial pre-stress of the unrusted steel strand
  • E p is the elastic modulus of the steel strand
  • the stress inside the corroded steel wire gradually increases along the component direction until the effective prestress is reached.
  • the strain change of the concrete at the position of the steel wire ⁇ c, i needs to be equal to the corroded steel wire
  • the strain change ⁇ p, i satisfies the strain coordination relationship, and the relationship is formula (21):
  • e p is the eccentricity of the steel strand
  • A is the cross-sectional area of the concrete
  • I is the moment of inertia of the section of the concrete.
  • the present invention mainly studies the influence of the corrosion of the steel strand on the prestress loss. It is assumed that no corrosion occurs in ordinary steel bars.
  • the strain distribution in the cross-section of the component is shown in Figure 3.
  • Strain, ⁇ s, i and ⁇ ′ s, i are formulas (23) and (24), respectively:
  • h x , a p and a s are the sectional centroids of the component, the center of gravity of the strand and the distance from the center of gravity of the tensile reinforcement to the bottom of the component, and a ′ s is the distance from the center of gravity of the compressed steel to the top of the component.
  • f s is the stress of ordinary steel bars
  • E s and E sp are the elastic modulus and strengthening modulus of ordinary steel bars, respectively
  • f sy and ⁇ sy are the yield strength and yield strain of ordinary steel bars, respectively.
  • a s and A ′ s are the cross-sectional areas of the common steel bars in the tension zone and the compression zone, respectively, and f s ( ⁇ s, i ) and f s ( ⁇ ′ s, i ) are the tension zone and compression, respectively. Area of the stress of ordinary reinforcement.
  • the mechanical behavior of tensile steel bars can be simulated by a linear elastic constitutive model, the mechanical behavior of compressed concrete can be described by a nonlinear constitutive model, and the stress-strain curve of concrete can be expressed as formula (28):
  • f c and ⁇ c are the stress and strain of the concrete
  • f ′ c is the uniaxial compressive strength of the concrete
  • ⁇ 0 is the corresponding strain when the concrete reaches the compressive strength, and its value is 0.002.
  • a c is the cross-sectional area of the damaged concrete.
  • the method for predicting the prestress loss after cracking along the tendons of the concrete proposed by the present invention can comprehensively consider the influence of factors such as concrete cracking and adhesion degradation caused by corrosion.
  • the calculation process of the corrosion prestress loss is as follows: First, the rust expansion cracking and adhesion degradation of the concrete are evaluated according to the degree of corrosion of the steel strand; then, the stress change of the corroded steel strand of any unit is calculated based on equation (17).
  • Equation (16) accumulates the internal stress increment of the steel strand; secondly, when the stress state of the prestressed steel strand, concrete, and ordinary reinforcing steel meets the strain coordination and stress balance equation, the accumulation of the internal stress of the steel strand is stopped ; Finally, the effective prestress of the corroded steel strand can be evaluated by equation (18). When the rust rate is taken as zero in the above calculation, the calculated result is the effective prestress of the unrusted steel strand.
  • the rust prestress loss of the present invention is defined as the effective prestress of the unrusted steel strand minus the effective prestress of the rusted steel strand.
  • Figure 4 shows the calculation flow chart of corrosion prestress loss.
  • the thickness of the protective layer of ordinary steel bar and steel strand is 30mm and 42.4mm, respectively.
  • the stirrups are made of HPB235 light round steel bars with a diameter of 6mm, and the spacing is 100mm.
  • the 28-day average uniaxial compressive strength of concrete is 44.1 MPa.
  • the detailed dimensions of the test beam are shown in Figure 5.
  • a DC power supply was used to rust the steel stranded wire, and the rust current was 0.1A.
  • the test beam was loaded with a four-point bending test device, as shown in FIG. 6. The distance between the loading points of the test beam supports is 1800mm, and the span of the pure bend is 600mm. After the end of the loading test, the average mass loss rate of the steel strands was used to evaluate the degree of corrosion. Table 1 shows the average mass loss rate of each test beam.
  • ⁇ is the average mass loss rate
  • F c is the test cracking load
  • F e, t is the effective pre-stress of the test
  • f e, t is the effective pre-stress of the test.
  • the tensile stress of the concrete at the bottom of the test beam is mainly controlled by the following three factors: the dead weight of the test beam, the effective prestress, and the applied load.
  • the dead weight of the test beam exceeds the tensile strength of the concrete, cracks appear in the bottom concrete.
  • the critical condition of cracking of the bottom concrete can be expressed as formula (31)
  • f p and ⁇ are the effective prestress of the corroded beam
  • y b is the distance from the bottom of the beam to the neutral axis
  • M s is the bending moment generated by the test beam's own weight
  • M c is the cracking moment
  • I c is the loss of concrete Moment of inertia.
  • the effective prestress and prestress loss of the rust test beam can be evaluated by using equation (31). The relevant results are shown in Table 1.
  • the prestress loss rate in Table 1 is defined as the rust prestress loss Ratio to initial prestress.
  • FIG. 7 shows the predicted and experimental values of the effective prestress of the test beam.
  • the standard prestress in the figure is defined as the effective prestress of the corroded steel strand and the 0.75f p ratio.
  • the average prediction error between the predicted value and the experimental value is 4.8%.
  • Table 1 gives the theoretical prestress loss rate and experimental prestress loss rate. The data of the two are relatively close, which proves the validity of the calculation method.
  • the above analysis shows that the prestress loss calculation method proposed by the present invention can reasonably predict the prestress loss of a rusted pre-tensioned concrete beam.

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Abstract

本发明公开的一种预测混凝土顺筋开裂后预应力损失方法，通过采用厚壁薄筒理论对混凝土的锈胀开裂进行模拟，基于开裂混凝土的剩余拉应力和未开裂混凝土的约束力对开裂过程中的锈胀力进行计算；分析钢绞线锈蚀对界面间的胶着力、混凝土约束力和锈胀力等因素的影响，构建锈蚀钢绞线的粘结强度计算表达式；综合考虑锈蚀引起的混凝土开裂和粘结强度退化等因素的耦合作用，基于应变协调及受力平衡方程建立锈蚀先张混凝土构件预应力损失的计算方法；本发明提出的一种预测混凝土顺筋开裂后预应力损失方法可综合考虑锈蚀引起的混凝土开裂及粘结退化等因素的耦合作用，对既有先张混凝土梁桥预应力损失的评估具有重要地指导意义。

Description

一种预测混凝土顺筋开裂后预应力损失方法 技术领域
本发明涉及预应力损失评估方法技术领域，具体是一种预测混凝土顺筋开裂后预应力损失方法。
背景技术
长期以来，预应力混凝土构件被认为具有良好的耐久性。然由于设计缺陷、不良施工和不利侵蚀环境等因素的影响，预应力混凝土构件性能劣化问题已日益显著。预应力筋锈蚀是造成结构耐久性退化的主要因素之一，锈蚀会减小预应力筋的截面面积、导致混凝土开裂、降低粘结强度，引起有效预应力的损失。合理评估混凝土构件内部的有效预应力是确保其正常使用和安全服役的关键因素。
既有混凝土构件的预应力损失与众多因素有关，如混凝土的收缩徐变、预应力钢绞线的应力松弛及锈蚀等。目前，针对混凝土收缩徐变、预应力钢绞线应力松弛等因素对长期预应力损失的影响已展开了大量的研究，部分规范也给出了长期预应力损失的评估方法。相对于混凝土构件长期预应力损失的报道，关于锈蚀预应力损失的研究相对较少。部分学者采用应变协调的方法评估了后张混凝土梁的残余预应力，也有学者指出后张混凝土梁的剩余预加力可通过锈蚀钢绞线的截面积进行估计。现有研究主要分析了锈蚀钢绞线截面积减小对后张混凝土构件预应力损失的影响。钢绞线锈蚀引起的预应力损失是一个十分复杂的问题，不仅仅是钢绞线截面积的减小会引起预应力损失，混凝土的锈胀开裂和粘结强度也会造成预应力损失。此外，后张混凝土构件依靠锚固系统进行预应力的传递，而先张预应力混凝土构件则通过钢绞线与混凝土间的粘结力来进行预应力传递，锈蚀粘结退化对先张混凝土构件有效预应力的影响会比后张 混凝土构件的影响要大。对于先张混凝土构件锈蚀后的预应力损失研究目前尚未见报道，如何合理地评估锈蚀先张混凝土构件内部的预应力损失有待进一步地研究。
为此，本发明提出了一种预测混凝土顺筋开裂后预应力损失方法，该方法的优势在于可综合考虑锈蚀引起的混凝土开裂及粘结退化等因素对先张混凝土构件内部预应力损失的影响。
发明内容
本发明的目的在于提供一种预测混凝土顺筋开裂后预应力损失方法，其可合理地评估锈蚀先张混凝土构件内部的预应力损失。
为有效解决上述技术问题，本发明采取的技术方案如下：
一种预测混凝土顺筋开裂后预应力损失方法，包括以下步骤：
(1)预测混凝土锈胀开裂：根据构件基本尺寸，确定几何参数取值，采用厚壁薄筒理论对混凝土的锈胀开裂进行模拟，锈胀开裂过程中，通过开裂混凝土的剩余拉应力和未开裂混凝土的约束力对锈胀力进行预测；
(2)分析锈蚀钢绞线粘结强度退化：建立钢绞线与混凝土界面间胶着力、约束力和锈胀力的表达式，分析钢绞线锈蚀对以上各因素的影响，进而计算锈蚀钢绞线粘结强度；
(3)评估锈蚀引起的预应力损失：将先张混凝土构件离散为多个微分单元，分析锈蚀钢绞线的内部应力传递规律，考虑混凝土锈胀开裂及粘结退化等因素的影响，基于应变协调及受力平衡方程建立锈蚀先张混凝土构件有效预应力的计算方法，进而对锈蚀预应力损失进行评估。
优选的，所述步骤(1)中，混凝土锈胀开裂过程中，锈胀力的计算如下：
保护层开裂前，锈胀力主要由开裂混凝土的剩余拉应力和未开裂混凝土的 约束力共同抵抗，钢绞线-混凝土界面间的锈胀力P c可表示为公式(1)：
Figure PCTCN2019084103-appb-000001
式中，R 0为锈蚀前钢丝的半径，P u为开裂和未开裂混凝土交界面位置的锈胀力，R u为开裂混凝土的半径，r为开裂混凝土区域的位置，σ θ(r)为开裂混凝土的环向应力；
保护层开裂后，锈胀力主要由开裂混凝土的剩余拉应力来抵抗，钢绞线-混凝土界面间的锈胀力P c可表示为公式(2)：
Figure PCTCN2019084103-appb-000002
优选的，所述步骤(2)中，锈蚀钢绞线粘结强度的计算如下：
锈蚀钢绞线的粘结强度主要由钢绞线与混凝土交界面间的胶着力、约束力和锈胀力来提供，其表达式为公式(3)：
τ η＝τ a+τ b+τ c
式中，τ η为锈蚀钢绞线的粘结应力，τ a为锈胀力引起的粘结应力，τ b为交界面间的胶着力，τ c为交界面间的约束力；
锈蚀钢绞线与混凝土交界面锈胀力引起的粘结应力可表示为公式(4)：
τ a＝k cp c
式中，k c为锈蚀钢绞线与混凝土界面间的摩擦系数；
锈蚀钢绞线与混凝土交界面间的胶着力可表达为公式(5)：
Figure PCTCN2019084103-appb-000003
式中，k为同一截面上钢绞线的横肋数目，A r为横肋面积，D为锈蚀钢绞线直径，δ为横肋与钢绞线轴线间的夹角，θ为钢绞线与混凝土间的摩擦角，s r为横 肋间距，f coh为界面间胶着力系数；
锈蚀钢绞线与混凝土交界面间周围混凝土的约束力可表达为公式(6)：
Figure PCTCN2019084103-appb-000004
式中，C r为横肋的形状系数，p x为失效时钢绞线所受的最大压力。
优选的，所述步骤(3)中，锈蚀先张混凝土构件有效预应力的计算方法如下：
将先张混凝土构件离散为多个微分单元，微分单元编号为1到n，对于单元i，其内部钢绞线的应力f p，i可表示为公式(7)：
f p，i＝f p，i+1-Δf p，i
式中，Δf p，i为锈蚀钢绞线单元i的局部应力变量，1≤i≤n；
单元i的局部应力变量Δf p，i可表示为公式(8)：
Figure PCTCN2019084103-appb-000005
式中，τ η为锈蚀钢绞线的粘结应力，l i为单元长度，A p，i(η)为单元i位置处锈蚀钢绞线的剩余截面积，R ρ，i为单元i位置处锈蚀钢丝的剩余半径；
对于锈蚀先张混凝土构件，构件端部位置处钢绞线的应力为0，即f p，1＝0，单元i位置处钢绞线的张拉应力f p，i可表示为公式(9)：
Figure PCTCN2019084103-appb-000006
单元i位置处锈蚀钢绞线的张拉力T p，i可表示为公式(10)：
T p，i＝f p，iA p，i(η)
单元i位置处钢绞线锈蚀前后的应变变化Δε p，i可表示为公式(11)：
Figure PCTCN2019084103-appb-000007
式中，T pi为未锈蚀钢绞线的初始预加力，E p为钢绞线的弹性模量；
锈蚀钢绞线内部的应力沿构件方向逐渐增加直至达到有效预应力，当锈蚀钢绞线的应力达到有效预应力时，钢绞线位置处混凝土的应变变化Δε c，i需等于锈蚀钢绞线的应变变化Δε p，i以满足应变协调关系，其关系为公式(12)：
Δε c，i＝Δε p，i
当锈蚀钢绞线的应力达到有效预应力时，预应力钢绞线、混凝土和普通钢筋的合力需满足平衡方程，可表示为公式(13)：
C i+F′ s，i-T p，i-F s，i＝0
考虑混凝土锈胀开裂及粘结退化等因素的影响，基于应变协调及受力平衡方程可建立锈蚀先张混凝土构件有效预应力的计算方法，进而可对锈蚀预应力损失进行评估。
本发明的有益效果为：本发明提供的一种预测混凝土顺筋开裂后预应力损失方法，通过采用厚壁薄筒理论对混凝土的锈胀开裂进行模拟，基于开裂混凝土的剩余拉应力和未开裂混凝土的约束力对开裂过程中的锈胀力进行计算；分析钢绞线锈蚀对界面间的胶着力、混凝土约束力和锈胀力等因素的影响，构建锈蚀钢绞线的粘结强度计算表达式；综合考虑锈蚀引起的混凝土开裂和粘结强度退化等因素的耦合作用，建立锈蚀先张混凝土构件预应力损失的评估方法；本发明提出的一种预测混凝土顺筋开裂后预应力损失方法，其优越性为可综合考虑锈蚀引起的混凝土开裂及粘结退化等因素的影响，能够对先张混凝土构件锈胀开裂后预应力损失进行合理地评估，计算结果可靠，可广泛应用于工程实际。
为更清楚地阐述本发明的特征和功效，下面结合附图与具体实施例来对本发明进行详细说明：
附图说明
图1是本发明钢绞线锈蚀引起的混凝土开裂示意图；
图2是本发明锈蚀钢绞线内部应力的变化；
图3是本发明构件横断面内的应变分布；
图4是本发明锈蚀预应力损失计算流程示意图；
图5是本发明试验梁的详细尺寸；
图6是本发明四点弯曲加载试验示意图；
图7(a)是本发明A组有效预应力的预测值和试验值；
图7(b)是本发明B组有效预应力的预测值和试验值。
具体实施方式
本发明揭示了一种预测混凝土顺筋开裂后预应力损失方法，包括有以下步骤：
(1)预测混凝土锈胀开裂：根据构件基本尺寸，确定几何参数取值，采用厚壁薄筒理论对混凝土的锈胀开裂进行模拟，锈胀开裂过程中，通过开裂混凝土的剩余拉应力和未开裂混凝土的约束力对锈胀力进行预测。
(2)分析锈蚀钢绞线粘结强度退化：建立钢绞线与混凝土界面间胶着力、约束力和锈胀力的表达式，分析钢绞线锈蚀对以上各因素的影响，进而计算锈蚀钢绞线粘结强度。
(3)评估锈蚀引起的预应力损失：将先张混凝土构件离散为多个微分单元，分析锈蚀钢绞线的内部应力传递规律，考虑混凝土锈胀开裂及粘结退化等因素的影响，基于应变协调及受力平衡方程建立锈蚀先张混凝土构件有效预应力的 计算方法，进而对锈蚀预应力损失进行评估。
所述步骤(1)中混凝土锈胀开裂过程中，锈胀力的表达式为：
以7丝钢绞线为研究对象，当钢绞线遭受外界物质侵蚀时，外围钢丝首先发生锈蚀，如图1所示，假定单根外围钢丝的锈蚀部位为周长的2/3，单根外围钢丝的面积损失为
Figure PCTCN2019084103-appb-000008
钢绞线的锈蚀率ρ可表示为公式(1)：
Figure PCTCN2019084103-appb-000009
式中，R 0和R ρ分别为锈蚀前后钢丝的半径，A p为未锈蚀钢绞线的截面面积。
钢绞线锈蚀产物的体积比相应消耗的铁的体积要大，这会导致锈蚀产物的向外膨胀。锈蚀产物一部分会填充混凝土内部的孔隙和裂缝，另外部分则会产生锈胀力。根据体积相等原则，单位长度上钢绞线锈蚀产物的总体积可表达为公式(2)：
ΔV t＝ΔV w+ΔV e+ΔV c
式中，ΔV t为单位长度上锈蚀产物的总体积，ΔV t＝nΔV w，n为铁锈膨胀率，其值取为3，ΔV w为单位长度上钢绞线外围钢丝的体积变化，
Figure PCTCN2019084103-appb-000010
ΔV e为单位长度上混凝土的体积变化，
Figure PCTCN2019084103-appb-000011
R t为包含锈蚀产物影响的钢丝半径，ΔV c为单位长度上填充裂缝和孔隙的锈蚀产物体积。
单位长度上填充裂缝和孔隙的锈蚀产物体积可表达为公式(3)：
Figure PCTCN2019084103-appb-000012
式中，R u为开裂混凝土的半径。
联立式(1-3)，锈胀力引起的混凝土位移u c可表示为公式(4)：
Figure PCTCN2019084103-appb-000013
保护层开裂前，混凝土保护层由开裂内环和未开裂外环组成，如图1所示。对于未开裂混凝土外环，可采用弹性理论对混凝土的内部应力进行模拟，未开裂混凝土的环向应力σ θ(t)和径向位移u(t)可分别表示为公式(5)及(6)：
Figure PCTCN2019084103-appb-000014
Figure PCTCN2019084103-appb-000015
式中，t为未开裂混凝土区域，R u≤t≤R c，R c＝R o+C，C为混凝土保护层厚度，P u为开裂和未开裂混凝土交界面位置的锈胀力，E c和v c分别为混凝土的弹性模量和泊松比。
根据应力分布协调原则，开裂与未开裂混凝土交界面位置处的应力需等于混凝土抗拉强度，即σ θ(R u)＝f t。由此可知，开裂与未开裂混凝土交界面的锈胀力P u可表示为公式(7)：
Figure PCTCN2019084103-appb-000016
联立式(6-7)，可得到未开裂混凝土的径向位移u(t)。假定开裂混凝土区域的径向位移满足线性分布原则，则开裂区混凝土的径向位移u(r)可表示为公式(8)：
Figure PCTCN2019084103-appb-000017
式中，r为开裂区混凝土的位置，R 0≤r≤R u。
考虑开裂混凝土抗拉强度的软化行为，其环向应力可表示为公式(9)：
Figure PCTCN2019084103-appb-000018
式中，σ θ(r)和ε θ(r)分别为混凝土环向应力和应变，ε ct为混凝土达到抗拉强度时所对应的应变，ε 1为混凝土应力为15％抗拉强度时所对应的应变，ε u为混凝土极限应变。
保护层开裂前，钢绞线-混凝土界面间的锈胀力P c主要由开裂混凝土的剩余拉应力和未开裂混凝土的约束力进行抵抗，可表示为公式(10)：
Figure PCTCN2019084103-appb-000019
式中，R 0为锈蚀前钢丝的半径，R u为开裂混凝土的半径，r为开裂区域混凝土的位置。
当裂缝扩展到混凝土表面时，开裂区域的半径等于保护层厚度，即R u＝R c。保护层开裂后，锈胀力主要由开裂混凝土的剩余拉应力来抵抗，钢绞线-混凝土界面的锈胀力P c可表示为公式(11)：
Figure PCTCN2019084103-appb-000020
所述步骤(2)中锈蚀钢绞线粘结强度的计算方法为：
锈蚀钢绞线的粘结强度可由钢绞线与混凝土交界面的胶着力、约束力和锈胀力进行计算，其表达式如公式(12)：
             τ η＝τ a+τ b+τ c
式中，τ η为锈蚀钢绞线的粘结应力，τ a为锈胀力引起的粘结应力，τ b为交界面的胶着力，τ c为交界面的约束力。
锈蚀钢绞线与混凝土交界面锈胀力引起的粘结应力可表示为公式(13)：
τ a＝k cp c
式中，k c为锈蚀钢绞线与混凝土界面间的摩擦系数，k c＝0.37-0.26(x-x cr)，x为钢绞线的锈蚀深度，x cr为保护层开裂的临界锈蚀深度。
锈蚀钢绞线与混凝土交界面的胶着力可表达为公式(14)：
Figure PCTCN2019084103-appb-000021
式中，k为同一截面上钢绞线的横肋数目，k＝2，A r为横肋面积，A r＝0.07πD 2， D为锈蚀钢绞线直径，δ为横肋与钢绞线轴线间的夹角，δ＝45°，θ为钢绞线与混凝土间的摩擦角，tan(δ+θ)＝1.57-0.785x，s r为横肋间距，s r＝0.6D，f coh为界面间胶着力系数，f coh＝2-10(x-x cr)。
锈蚀钢绞线与混凝土交界面周围混凝土的约束力可表达为公式(15)：
Figure PCTCN2019084103-appb-000022
式中，C r为横肋的形状系数，C r＝0.8，p x为失效时钢绞线所受的最大压力。
所述步骤(3)中有效预应力的计算方法为：
将先张混凝土构件离散为多个微分单元，微分单元编号为1到n，图2给出了锈蚀钢绞线内部应力的传递示意图，对于单元i，其内部钢绞线的应力f p，i可表示为公式(16)：
f p，i＝f p，i+1-Δf p，i
式中，Δf p，i为锈蚀钢绞线单元i的局部应力变量，1≤i≤n。
单元i的局部应力变量Δf p，i可表示为公式(17)：
Figure PCTCN2019084103-appb-000023
式中，l i为单元长度，A p，i(η)为单元i位置处锈蚀钢绞线的剩余截面积，R ρ，i为单元i位置处锈蚀钢丝的剩余半径。
对于先张混凝土构件，构件端部位置处钢绞线的应力为0，即f p，1＝0，单元i位置处钢绞线的张拉应力f p，i可表示为公式(18)：
Figure PCTCN2019084103-appb-000024
单元i位置处锈蚀钢绞线的张拉力T p，i可表示为公式(19)：
T p，i＝f p，iA p，i(η)
单元i位置处钢绞线锈蚀前后的应变变化Δε p，i可表示为公式(20)：
Figure PCTCN2019084103-appb-000025
式中，T pi为未锈蚀钢绞线的初始预加力，E p为钢绞线的弹性模量。
锈蚀钢绞线内部的应力沿构件方向逐渐增加直至达到有效预应力，当锈蚀钢绞线的应力达到有效预应力时，钢绞线位置处混凝土的应变变化Δε c，i需等于锈蚀钢绞线的应变变化Δε p，i以满足应变协调关系，其关系为公式(21)：
Δε c，i＝Δε p，i
锈蚀钢绞线位置处的混凝土应变ε cp，i可表示为公式(22)：
Figure PCTCN2019084103-appb-000026
式中，e p为钢绞线的偏心距，A为混凝土的横断面面积，I为混凝土的截面惯性矩。
本发明主要研究钢绞线锈蚀对预应力损失的影响，普通钢筋假定其未发生锈蚀，构件横断面内的应变分布如图3所示，单元i位置处受拉区和受压区普通钢筋的应变，ε s，i和ε′ s，i，分别为公式(23)和(24)：
Figure PCTCN2019084103-appb-000027
Figure PCTCN2019084103-appb-000028
式中，h x，a p和a s分别为构件的截面形心，钢绞线重心和受拉钢筋重心至构件底部的距离，a′ s为受压钢筋重心至构件顶部的距离。
普通钢筋的应力-应变关系可以通过弹塑性本构模型进行描述，其表达式为公式(25)：
Figure PCTCN2019084103-appb-000029
式中，f s为普通钢筋的应力，E s和E sp分别为普通钢筋的弹性模量和强化模量，f sy和ε sy分别为普通钢筋的屈服强度和屈服应变。
单元i位置处受拉区和受压区普通钢筋的合力，F s，i和F′ s，i，可分别表示为公式(26)和(27)：
F s，i＝A sf s(ε s，i)
F′ s，i＝A′ sf s(ε′ s，i)
式中，A s和A′ s分别为受拉区和受压区普通钢筋的截面面积，f s(ε s，i)和f s(ε′ s，i)分别为受拉区和受压区普通钢筋的应力。
受拉钢筋的力学行为可通过线弹性本构模型进行模拟，受压混凝土的力学行为可通过非线性本构模型来进行描述，混凝土的应力-应变曲线可表示为公式(28)：
Figure PCTCN2019084103-appb-000030
式中，f c和ε c分别为混凝土的应力和应变，f′ c为混凝土单轴抗压强度，ε 0为混凝土达到抗压强度时所对应的应变，其值为0.002。
单元i位置处混凝土的合力C i可表示为公式(29)：
Figure PCTCN2019084103-appb-000031
式中，A c为损伤混凝土的截面面积。
当锈蚀钢绞线的应力达到有效预应力时，预应力钢绞线、混凝土和普通钢筋的合力需满足平衡方程，可表示为公式(30)：
C i+F′ s，i-T p，i-F s，i＝0
综上所述，本发明提出的一种预测混凝土顺筋开裂后预应力损失方法可综合考虑锈蚀引起的混凝土开裂及粘结退化等因素的影响。锈蚀预应力损失的计算流程如下：首先，根据钢绞线锈蚀程度，对混凝土的锈胀开裂和粘结退化进行评估；然后，基于式(17)计算任意单元锈蚀钢绞线的应力变化，使用式(16)对钢绞线内部应力增量进行累加；其次，当预应力钢绞线、混凝土和普通钢筋的应力状态满足应变协调和受力平衡方程时，停止对钢绞线内部应力的累加；最后，锈蚀钢绞线的有效预应力可通过式(18)进行评估。当上述计算中锈蚀率取为零时，计算得到的结果即为未锈蚀钢绞线的有效预应力。本发明的锈蚀预应力损失定义为未锈蚀钢绞线的有效预应力减去锈蚀钢绞线的有效预应力。图4给出了锈蚀预应力损失的计算流程示意图。
为评估不同应力状态下锈蚀先张混凝土梁的预应力损失，设计制作了6片横断面尺寸为130×150mm，长为2000mm的先张预应力混凝土梁。试验梁底部配有1根直径为15.2mm的7丝钢绞线和2根直径为6mm的HRB400变形钢筋，顶部配有2根直径为8mm的HRB400变形钢筋。钢绞线的屈服强度和极限强度分别为1830MPa和1910MPa，变形钢筋的屈服强度和极限强度分别为400MPa和540MPa。普通钢筋和钢绞线的保护层厚度分别为30mm和42.4mm。箍筋采用直径为6mm的HPB235光圆钢筋，间距为100mm。混凝土28天的平均单轴抗压强度强度为44.1MPa。试验梁的详细尺寸如图5所示。
为研究不同应力状态和不同锈蚀程度下试验梁预应力损失的变化规律，根据不同的锈蚀时间分别设计了A、B两组构件，A、B组的锈蚀时间分别为15和20天，每组中各设计了三种不同应力状态下的试验梁。以A组为例，PA1、PA2和PA3的应力大小分别为0.25f p，0.5f p，和0.75f p，其中f p为1860MPa。试验过程中采用电化学加速锈蚀方法对钢绞线进行锈蚀，为单独研究钢绞线锈蚀对预应力损失的影响，利用环氧树脂对普通钢筋进行防锈处理。采用直流电源对钢绞线进行锈蚀，锈蚀电流为0.1A。加速锈蚀后，采用四点弯曲试验装置对试验梁进行加载，如图6所示。试验梁支座加载点的距离为1800mm，跨中纯弯段为600mm。加载测试结束后，采用钢绞线的平均质量损失率对其锈蚀程度进行评估，表1给出了各试验梁的平均质量损失率。
表1试验测量结果汇总
Figure PCTCN2019084103-appb-000032
注：ρ为平均质量损失率，F c为试验开裂荷载，F e，t为试验有效预加力，f e，t为试验有效预应力。
加载期间，试验梁底部混凝土的张拉应力主要由以下三个因素控制：试验梁的自重，有效预应力和外加荷载。当梁底的张拉应力超过混凝土的抗拉强度时，底部混凝土出现裂缝。底部混凝土开裂的临界条件可表示为公式(31)
Figure PCTCN2019084103-appb-000033
式中，f p，η为锈蚀梁的有效预应力，y b为梁底至中和轴的距离，M s为试验梁自重产生的弯矩，M c为开裂弯矩，I c为损失混凝土的惯性矩。
基于上述测量得到的开裂荷载和锈蚀率，利用式(31)可以评估锈蚀试验梁的有效预应力和预应力损失，相关结果见表1，表1中的预应力损失率定义为锈蚀预应力损失与初始预应力之比。
利用本发明提出的计算方法对试验结果进行预测，图7给出了试验梁有效预应力的预测值和试验值，图中标准预应力定义为锈蚀钢绞线的有效预应力与0.75f p之比。由图7可知，预测值和试验值之间的平均预测误差为4.8％。此外，表1给出了理论预应力损失率和试验预应力损失率，两者数据较为接近，证明了该计算方法的有效性。以上分析表明，本发明提出的预应力损失计算方法可以合理地预测锈蚀先张混凝土梁的预应力损失。
以上结合具体实施例描述了本发明的技术原理。这些描述只是为了解释本发明的原理，而不能以任何方式解释为对本发明保护范围的限制。基于此处的解释，本领域的技术人员不需要付出创造性的劳动即可联想到本发明的其它具体实施方式，这些方式都将落入本发明的保护范围之内。

Claims (4)

  1. 一种预测混凝土顺筋开裂后预应力损失方法，其特征在于，包括以下步骤：
    (1)预测混凝土锈胀开裂：根据构件基本尺寸，确定几何参数取值，采用厚壁薄筒理论对混凝土的锈胀开裂进行模拟，锈胀开裂过程中，通过开裂混凝土的剩余拉应力和未开裂混凝土的约束力对锈胀力进行预测；
    (2)分析锈蚀钢绞线粘结强度退化：建立钢绞线与混凝土界面间胶着力、约束力和锈胀力的表达式，分析钢绞线锈蚀对以上各因素的影响，进而计算锈蚀钢绞线粘结强度；
    (3)评估锈蚀引起的预应力损失：将先张混凝土构件离散为多个微分单元，分析锈蚀钢绞线的内部应力传递规律，考虑混凝土锈胀开裂及粘结退化因素的影响，基于应变协调及受力平衡方程建立锈蚀先张混凝土构件有效预应力的计算方法，进而对锈蚀预应力损失进行评估。
  2. 如权利要求1所述一种预测混凝土顺筋开裂后预应力损失方法，其特征在于：所述步骤(1)中，混凝土锈胀开裂过程中，锈胀力的计算如下：
    保护层开裂前，锈胀力主要由开裂混凝土的剩余拉应力和未开裂混凝土的约束力共同抵抗，钢绞线-混凝土界面间的锈胀力P c可表示为公式(1)：
    Figure PCTCN2019084103-appb-100001
    式中，R 0为锈蚀前钢丝的半径，P u为开裂和未开裂混凝土交界面位置的锈胀力，R u为开裂混凝土的半径，r为开裂混凝土区域的位置，σ θ(r)为开裂混凝土的环向应力；
    保护层开裂后，锈胀力主要由开裂混凝土的剩余拉应力来抵抗，钢绞线-混凝土界面间的锈胀力P c可表示为公式(2)：
    Figure PCTCN2019084103-appb-100002
  3. 如权利要求1所述一种预测混凝土顺筋开裂后预应力损失方法，其特征在于：所述步骤(2)中，锈蚀钢绞线粘结强度的计算如下：
    锈蚀钢绞线的粘结强度主要由钢绞线与混凝土交界面间的胶着力、约束力和锈胀力来提供，其表达式为公式(3)：
    τ η＝τ a+τ b+τ c
    式中，τ η为锈蚀钢绞线的粘结应力，τ a为锈胀力引起的粘结应力，τ b为交界面间的胶着力，τ c为交界面间的约束力；
    锈蚀钢绞线与混凝土交界面锈胀力引起的粘结应力表示为公式(4)：
    τ a＝k cp c
    式中，k c为锈蚀钢绞线与混凝土界面间的摩擦系数；
    锈蚀钢绞线与混凝土交界面间的胶着力表达为公式(5)：
    Figure PCTCN2019084103-appb-100003
    式中，k为同一截面上钢绞线的横肋数目，A r为横肋面积，D为锈蚀钢绞线直径，δ为横肋与钢绞线轴线间的夹角，θ为钢绞线与混凝土间的摩擦角，s r为横肋间距，f coh为界面间胶着力系数；
    锈蚀钢绞线与混凝土交界面间周围混凝土的约束力表达为公式(6)：
    Figure PCTCN2019084103-appb-100004
    式中，C r为横肋的形状系数，p x为失效时钢绞线所受的最大压力。
  4. 如权利要求1所述一种预测混凝土顺筋开裂后预应力损失方法，其特征在于：所述步骤(3)中，锈蚀先张混凝土构件有效预应力的计算方法如下：
    将先张混凝土构件离散为多个微分单元，微分单元编号为1到n，对于单元i，其内部钢绞线的应力f p，i表示为公式(7)：
    f p，i＝f p，i+1-Δf p，i
    式中，Δf p，i为锈蚀钢绞线单元i的局部应力变量，1≤i≤n；
    单元i的局部应力变量Δf p，i表示为公式(8)：
    Figure PCTCN2019084103-appb-100005
    式中，τ η为锈蚀钢绞线的粘结应力；l i为单元长度；A p，i(η)为单元i位置处锈蚀钢绞线的剩余截面积，R ρ，i为单元i位置处锈蚀钢丝的剩余半径；
    对于锈蚀先张预应力混凝土构件，构件端部位置处钢绞线的应力为0，即f p，1＝0，单元i位置处钢绞线的张拉应力f p，i表示为公式(9)：
    Figure PCTCN2019084103-appb-100006
    单元i位置处锈蚀钢绞线的张拉力T p，i表示为公式(10)：
    T p，i＝f p，iA p，i(η)
    单元i位置处钢绞线锈蚀前后的应变变化Δε p，i表示为公式(11)：
    Figure PCTCN2019084103-appb-100007
    式中，T pi为未锈蚀钢绞线的初始预加力，E p为钢绞线的弹性模量；
    锈蚀钢绞线的内部应力沿构件方向逐渐增加直至达到有效预应力，当锈蚀钢绞线的应力达到有效预应力时，钢绞线位置处混凝土的应变变化Δε c，i需等于锈蚀钢绞线的应变变化Δε p，i以满足应变协调关系，其关系为公式(12)：
    Δε c，i＝Δε p，i
    当锈蚀钢绞线的应力达到有效预应力时，预应力钢绞线、混凝土和普通钢筋的合力需满足平衡方程，表示为公式(13)：
    C i+F′ s，i-T p，i-F s，i＝0
    式中，C i为单元i位置处混凝土的合力，F s，i和F′ s，i分别为单元i位置处受拉区和受压区普通钢筋的合力；
    考虑混凝土锈胀开裂及粘结退化因素的影响，基于应变协调关系及受力平衡方程建立锈蚀先张混凝土构件有效预应力的计算方法，进而对锈蚀预应力损失进行评估。
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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114912273A (zh) * 2022-05-12 2022-08-16 苏州热工研究院有限公司 一种安全壳钢束预应力时限老化分析方法
CN116305947A (zh) * 2023-03-20 2023-06-23 中国石油大学(北京) 埋地管道应力预测方法、安全评估方法、设备和存储介质
WO2024046430A1 (zh) * 2022-08-31 2024-03-07 深圳大学 一种钢筋混凝土结构损伤定量监测方法及系统

Families Citing this family (13)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109190156B (zh) * 2018-07-26 2021-08-20 长沙理工大学 一种预测混凝土顺筋开裂后预应力损失方法
CN109669028B (zh) * 2019-03-04 2021-06-15 青岛理工大学 一种钢筋锈胀引起混凝土开裂锈胀力的测量方法
CN110108864B (zh) * 2019-05-21 2022-01-28 湖南城市学院 一种预应力混凝土梁无损检测系统及方法
CN111797458A (zh) * 2020-07-17 2020-10-20 浙江瓯越交建科技股份有限公司 早龄期预制混凝土结构零反拱的预应力分批张拉控制方法
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CN118171379A (zh) * 2024-05-15 2024-06-11 中冶建筑研究总院有限公司 复杂结构弹性压缩预应力损失逆向确定和正向补偿方法

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102323976A (zh) * 2011-06-24 2012-01-18 武汉理工大学 混凝土桥梁收缩徐变及预应力损失计算方法
CN104484551A (zh) * 2014-11-20 2015-04-01 哈尔滨工业大学 预应力混凝土梁板中无粘结筋极限应力增量的建模与计算方法
CN105825030A (zh) * 2016-04-01 2016-08-03 长沙理工大学 老化钢筋混凝土桥梁疲劳寿命评估方法
CN106021709A (zh) * 2016-05-18 2016-10-12 中建三局集团有限公司 一种混凝土早期开裂风险的评估和控制方法
CN109190156A (zh) * 2018-07-26 2019-01-11 长沙理工大学 一种预测混凝土顺筋开裂后预应力损失方法

Family Cites Families (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2012177284A (ja) * 2011-02-28 2012-09-13 Takenaka Komuten Co Ltd 鉄筋コンクリート壁のひび割れ制御方法
CN104198366B (zh) * 2014-09-01 2016-12-07 北京科技大学 一种后张预应力混凝土结构钢绞线锈蚀监测方法
CN104730222B (zh) * 2015-03-27 2017-01-18 交通运输部公路科学研究所 一种钢筋混凝土构件锈蚀开裂后钢筋锈蚀度无损检测方法

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102323976A (zh) * 2011-06-24 2012-01-18 武汉理工大学 混凝土桥梁收缩徐变及预应力损失计算方法
CN104484551A (zh) * 2014-11-20 2015-04-01 哈尔滨工业大学 预应力混凝土梁板中无粘结筋极限应力增量的建模与计算方法
CN105825030A (zh) * 2016-04-01 2016-08-03 长沙理工大学 老化钢筋混凝土桥梁疲劳寿命评估方法
CN106021709A (zh) * 2016-05-18 2016-10-12 中建三局集团有限公司 一种混凝土早期开裂风险的评估和控制方法
CN109190156A (zh) * 2018-07-26 2019-01-11 长沙理工大学 一种预测混凝土顺筋开裂后预应力损失方法

Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114912273A (zh) * 2022-05-12 2022-08-16 苏州热工研究院有限公司 一种安全壳钢束预应力时限老化分析方法
CN114912273B (zh) * 2022-05-12 2024-04-26 苏州热工研究院有限公司 一种安全壳钢束预应力时限老化分析方法
WO2024046430A1 (zh) * 2022-08-31 2024-03-07 深圳大学 一种钢筋混凝土结构损伤定量监测方法及系统
CN116305947A (zh) * 2023-03-20 2023-06-23 中国石油大学(北京) 埋地管道应力预测方法、安全评估方法、设备和存储介质
CN116305947B (zh) * 2023-03-20 2023-10-17 中国石油大学(北京) 埋地管道应力预测方法、安全评估方法、设备和存储介质

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